Théorème de Thalès

Claudy Diguet (claudy.diguet@tiscali.fr) - 14 novembre 2002

Les fichiers MetaPost

fig1.mp


u = 1cm;

beginfig(1);

pair A, B, C, M, N;
A=(0,0)*u; B=(1.5,2)*u; C=(4,0)*u; 
N=(1.9,0)*u; 
M=(0.65,1)*u;

draw A--B--C--cycle withpen pencircle scaled 1.5pt;
draw (0,1.6)*u 
for i=0 upto 3 :
..(i,-0.8*i+1.6)*u endfor withpen pencircle scaled 1.5pt;

label.lft("A",A);
label.rt("C",C);
label.top("B",B);
label.lft("M",M);
label.bot("N",N);

endfig;
end

fig2.mp


u = 1cm;

beginfig(1);

pair A, B, C, M, N, O;
A=(0,0)*u; B=(1.5,2)*u; C=(4,0)*u; 
N=(1.9,0)*u; 
M=(0.65,1)*u;
O=(3,-0.8)*u;

draw A--B--C--cycle withpen pencircle scaled 1.5pt;
draw (0,1.6)*u 
for i=0 upto 3 :
..(i,-0.8*i+1.6)*u endfor withpen pencircle scaled 1.5pt;

label.lft("A",A);
label.rt("C",C);
label.top("B",B);
label.lft("M",M);
label.bot("N",N);
label.rt(btex $(d)$ etex,O);

endfig;
end

fig3.mp


u = 0.7cm;

beginfig(1);

pair A, B, C, M, N, P, Q;
A=(0,0)*u; B=(-0.75,-3)*u; C=(1.5,-3)*u; 
M=(-0.5,-2)*u; 
N=(1,-2)*u;
P=(0.25,1)*u; Q=(-0.5,1)*u;

draw (0.25,1)*u--(-1,-4)*u withpen pencircle scaled 1pt;
draw (-1/2,1)*u--(2,-4)*u withpen pencircle scaled 1pt;
draw (-1,-2)*u--(1.5,-2)*u withpen pencircle scaled 1pt; 
draw (-1,-3)*u--(2,-3)*u withpen pencircle scaled 1pt;

label.lft("A",A);
label.urt("C",C);
label.ulft("B",B);
label.ulft("M",M);
label.urt("N",N);
label.rt("(d)",P);
label.lft("(d')",Q);

endfig;
end

fig3b.mp


u = 0.7cm;

beginfig(1);

pair A, B, C, M, N, P, Q;
A=(0,0)*u; M=(-0.75,-3)*u; N=(1.5,-3)*u; 
B=(-0.5,-2)*u; 
C=(1,-2)*u;
P=(0.25,1)*u; Q=(-0.5,1)*u;

draw (0.25,1)*u--(-1,-4)*u withpen pencircle scaled 1pt;
draw (-1/2,1)*u--(2,-4)*u withpen pencircle scaled 1pt;
draw (-1,-2)*u--(1.5,-2)*u withpen pencircle scaled 1pt; 
draw (-1,-3)*u--(2,-3)*u withpen pencircle scaled 1pt;

label.lft("A",A);
label.urt("C",C);
label.ulft("B",B);
label.ulft("M",M);
label.urt("N",N);
label.rt("(d)",P);
label.lft("(d')",Q);

endfig;
end

fig3bb.mp


u = 0.57cm;

beginfig(1);

pair A, B, C, M, N;
A=(0,0)*u; B=(-0.75,-3)*u; C=(1.5,-3)*u; 
M=(0.25,1)*u; 
N=(-0.5,1)*u;

draw (-0.8,1)*u--(1,1)*u withpen pencircle scaled 1pt;
draw (0.5,2)*u--(-1,-4)*u withpen pencircle scaled 1pt;
draw (2,-4)*u--(-1,2)*u withpen pencircle scaled 1pt; 
draw (-1,-3)*u--(2,-3)*u withpen pencircle scaled 1pt;

label.lft("A",A);
label.urt("C",C);
label.ulft("B",B);
label.lrt("M",M);
label.llft("N",N);
label.rt("(d)",(0.5,2)*u);
label.lft("(d')",(-1,2)*u);

endfig;
end

fig4.mp


u = 0.3cm;

beginfig(1);

pair A, B, C, D, O;
O=(0,0)*u; B=(4.35,0)*u; C=(-8.25,-3.3)*u; 
D=(-6,0)*u; 
A=(6.25,2.5)*u;

draw A--B withpen pencircle scaled 1.5pt;
draw C--D withpen pencircle scaled 1.5pt;
draw (-7,0)*u--(6,0)*u withpen pencircle scaled 1.5pt; 
draw (-9,-3.6)*u--(7,2.8)*u withpen pencircle scaled 1.5pt;

label.top("A",A);
label.bot("C",C);
label.bot("B",B);
label.top("O",O);
label.top("D",D);

endfig;
end

fig5.mp


u = 1cm;

beginfig(1);

pair A, B, C, M, N;
B=(0,0)*u; A=(1,4)*u; C=(5,0)*u; 
M=(2/3,8/3)*u; 
N=(2.33,2.67)*u;

draw A--B--C--cycle withpen pencircle scaled 1pt;
draw M--N withpen pencircle scaled 1pt;

label.top("A",A);
label.rt("C",C);
label.lft("B",B);
label.lft("M",M);
label.rt("N",N);

endfig;
end

fig6.mp


u = 1cm;

beginfig(1);

pair A, B, C, M, N, P, Q;
A=(0,0)*u; B=(-0.75,-3)*u; C=(1.5,-3)*u; 
M=(-0.5,-2)*u; 
N=(1,-2)*u;
P=(0.25,1)*u; Q=(-0.5,1)*u;

draw (0.25,1)*u--(-1,-4)*u withpen pencircle scaled 1pt;
draw (-1/2,1)*u--(2,-4)*u withpen pencircle scaled 1pt;
draw (-1,-2)*u--(1.5,-2)*u withpen pencircle scaled 1pt; 
draw (-1,-3)*u--(2,-3)*u withpen pencircle scaled 1pt;

label.lft("A",A);
label.urt("C",C);
label.ulft("B",B);
label.ulft("M",M);
label.urt("N",N);
label.rt("(d)",P);
label.lft("(d')",Q);

endfig;
end

Le document

Il s'agit d'un cours sur le théorème de Thalès et sa réciproque. Le source est disponible. Une prévisualisation du document et un fichier pdf sont accessibles ci-dessous.

Source index.txt mouliné par petitParseur(Z+B) le jeudi 14 novembre 2002.